Multiscale major factor selections for complex system data with structural dependency and heterogeneity

Unraveling Heterogeneity of ADNI’s Time-to-Event Data Using Conditional Entropy—Part I: Cross-Sectional Study

“…It is worth reiterating that, as mentioned in Section IV and previous work [13], any highly associative relationships among features would require extra computational efforts for explicitly and evaluating their joint conditional dependency or interacting effects much harder. We demonstrate why such required efforts are needed in this subsection by implementing our major factor selection protocol facilitated by contingency-table-based CE computations within this ADNI data set.…”

“…This paper proposes the Categorical Exploratory Data Analysis (CEDA) paradigm to algorithmically resolve all issues raised from Q1 through Q5 and partially Q6 and Q7 [11], [12], [13], [14]. In CEDA, we apply Shannon conditional entropy to evaluate associative relation, and mutual information to select so-called major factors underlying the dynamics of the response variable in relation to all covariate feature variables.…”

“…In this subsection, we briefly review the concept and computing of conditional entropy and mutual information as two key Theoretical Information Measurements used throughout this paper. Detailed derivations of related formulas of these two measurements are referred to previous works [11], [12], [13], [14]. We employ these two entropy-based measurements to evaluate potentially nonlinear directional association from a generic covariate feature variable denoted as X to a generic response variable denoted as Y, and the nondirectional association between two covariate feature variables, say X 1 and X 2 .…”

“…In order to resolve these two difficulties, a de-associating procedure is proposed [13] by simply subdividing the entire data set with respect to a target covariate variable's categories. For instance, A is the target covariate variable, and the entire data set is divided into h sub-collections with respect to {a 1 , .., a h }.…”

“…By summarizing all aforementioned developments in this subsection, we arrive at the CEDA's Major Factor Selection (MFS) protocol under two settings. The first setting is developed [11] to deal with independent or slightly dependent covariate feature variables only, while the second set is developed [13] to deal with the heavily dependent covariate setting. Nonetheless, by adopting the de-associating procedure within any heavily dependent setting, the MFS protocol originally built under an independent setting is indeed applied within the sub-collection levels, at which all heavily dependent covariate features indeed become much less dependent.…”